Nelson Rangel-Valdez

Construction of mixed covering arrays of variable strength using a tabu search approach

The development of a new system involves extensive tests on the software functionality in order to identify possible failures. Also, a system already built requires a fine tuning of its configurable options to give the best performance in the environment it is going to work. Both cases require a finite set of tests that avoids testing all the possible combinations (which is time consuming); to this situation Mixed Covering Arrays (MCAs) are a feasible alternative. MCAs are combinatorial structures represented as matrices having a test case per row. MCAs are small, in comparison with brute force, and guarantees a level of interaction among the parameters involved (a difference with random testing). We present a Tabu Search (TS) algorithm to construct MCAs; the novelty in the algorithm is a mixture of three neighborhood functions. We also present a new benchmark for the MCAs problem. The experimental evidence showed that the TS algorithm improves the results obtained by other approaches reported in the literature, finding the optimal solution in some the solved cases.

Strength Two Covering Arrays Construction Using a SAT Representation

According to the NIST report of 2002 there is a great potential to reduce the cost, and to increase the quality of the software developed in USA through the creation of automated tools that help in the software testing process. One alternative to improve the software testing process is the creation of tools that generate testing cases in an automatic way. Through the construction of Covering Arrays (CA) it is possible to obtain a minimum set of test cases with the maximum possibility of testing all the functionality of the developed software. n nIn this paper an approach to construct CA using the propositional satisfiability problem (SAT) is presented. The approach starts with the transformation of a CA instance into a non-conjunctive normal form (non-CNF) SAT instance. Then the SAT instance is solved through a non-CNF SAT solver, and finally the SAT solution is transformed into a CA solution. The main contributions of this work are: an efficient non-CNF SAT solver able to equals or improves previously reported results, and a simplified SAT representation to solve the CA problem.

CONSTRUCTION OF MIXED COVERING ARRAYS OF STRENGTHS 2 THROUGH 6 USING A TABU SEARCH APPROACH

The development of a new software system involves extensive tests of the software functionality in order to identify possible failures. Also, a software system already built requires a fine tuning of its configurable options to give the best performance in the environment where it is going to work. Both cases require a finite set of tests that avoids testing all the possible combinations (which is time consuming); to this situation mixed covering arrays (MCAs) are a feasible alternative. MCAs are combinatorial structures having a case per row. MCAs are small, in comparison with exhaustive search, and guarantee a level of interaction among the involved parameters (a difference with random testing). We present a tabu search algorithm (TSA) for the construction of MCAs. Also, we report the fine tuning process used to identify the best parameter values for TSA. The analyzed TSA parameters were three different initialization functions, five different tabu list sizes and the mixture of four neighborhood functio...

A heuristic approach for constructing ternary covering arrays using trinomial coefficients

This paper presents a simulated annealing (SA) algorithm for the construction of ternary covering arrays (CAs) using a trinomial coefficient representation. A ternary CA, denoted by CA(t, k, 3), is an N × k array where each N × t subarray contains each of the 3t combinations of symbols at least once. The construction of optimal CAs is, in general, an NP-complete problem. Many reported SA implementations use an N × k matrix representation for the CA construction. Instead of this, we represent ternary CAs using trinomial coefficients in order to reduce the search space for the SA algorithm.

Supercomputing and grid computing on the verification of covering arrays

The Covering Arrays (CAs) are mathematical objects with minimal coverage and maximum cardinality that are a good tool for the design of experiments. Axa0covering array is an N×k matrix over an alphabet v s.t. each N×k subset contains at least one time each combination from {0,1,…,v−1}t, given a positive integer valuexa0t. The process of ensuring that a CA contains each of the vt combinations is called verification of CA. In this paper, we present an algorithm for CA verification and its implementation details in three different computation paradigms: (a)xa0sequential approach (SA); (b)xa0parallel approach (PA); and (c)xa0Grid approach (GA). Four different PAs were compared in their performance of verifying a matrix as a CA; the PA with the best performance was included in a different experimentation where the three paradigms, SA, PA, and GA were compared in a benchmark composed by 45 possible CA instances. The results showed the limitations of the different paradigms when solving the verification of CA problem, and points out the necessity of a Grid approach to solve the problem when the size of a CA grows.

Construction of logarithm tables for Galois Fields

A branch of mathematics commonly used in cryptography is Galois Fields GF(p n ). Two basic operations performed in GF(p n ) are the addition and the multiplication. While the addition is generally easy to compute, the multiplication requires a special treatment. A well-known method to compute the multiplication is based on logarithm and antilogarithm tables. A primitive element of a GF(p n ) is a key part in the construction of such tables, but it is generally hard to find a primitive element for arbitrary values of p and n. This article presents a naive algorithm that can simultaneously find a primitive element of GF(p n ) and construct its corresponding logarithm and antilogarithm tables. The proposed algorithm was tested in GF(p n ) for several values of p and n; the results show a good performance, having an average time of 0.46 seconds to find the first primitive element of a given GF(p n ) for values of nu2009=u2009{2,u20093,u20094,u20095,u20098,u200912} and prime values p between 2 and 97.

Verification of general and cyclic covering arrays using grid computing

A covering array (CA) is an N × k matrix over the alphabet v s.t. each N × k subset contains at least one time each vt combination. Covering Arrays (CAs) have been applied mainly in software and hardware testing. The construction of CAs requires to do the verification that each N × t subset contains at least one time each vt combination. In this paper we present a sequential algorithm and a grid algorithm to do the CA verification. The algorithms were tested using a benchmark of CAs of variable strength. The main conclusion of the paper lies in the identification of the strengths and weakness of our algorithms (related to the values of the CA parameters).

An exact approach to maximize the number of wild cards in a covering array

Covering Arrays CA(N;t,k,v) are combinatorial structures that can be used to define adequate test suites for software testing. The smaller a CA is, the smaller the number of test cases that will be given to test the functionality of a software component in order to identify possible failures. Due to the fact that the construction of CAs of optimal size is a highly combinatorial problem, several approximated strategies have been developed. Some constructions of these strategies can be further improved through a post optimization process. For example, the wild card profile of a CA is the set of symbols that can be modified without changing the properties that define a CA. It has been shown that some CAs can be reduced by merging rows that contain wild cards. This paper presents a Branch and Bound (BB2,8,6) different profiles can be obtained; such profiles vary in the number of wild cards and their distribution in the CA.

Construction of Orthogonal Arrays of Index Unity Using Logarithm Tables for Galois Fields

Of particular interest in this chapter are the combinatorial objects called Orthogonal Arrays (OAs). These objects have been studied given of their wide range of applications in the industry, Gopalakrishnan & Stinson (2008) present their applications in computer science; among them are in the generation of error correcting codes presented by (Hedayat et al., 1999; Stinson, 2004), or in the design of experiments for software testing as shown by Taguchi (1994).

A metaheuristic optimization-based indirect elicitation of preference parameters for solving many-objective problems

A priori incorporation of the decision maker’s preferences is a crucial issue in many-objective evolutionary optimization. Some approaches characterize the best compromise solution of this problem through fuzzy outranking relations; however, they require the elicitation of a large number of parameters (weights and different thresholds). This paper proposes a novel metaheuristic-based optimization method to infer the model’s parameters of a fuzzy relational system of preferences, based on a small number of judgments given by the decision maker. The results show a satisfactory rate of error when predicting new outcomes with the parameter values obtained by using small size reference sets.